<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>mpt_demo_lti2</title>
<style type="text/css">
	body {background-color: white; color: black; font-family:sans-serif; font-size:medium;}
	a:link {color: #3300ff;}
	a:visited {color: #663399;}
	a:hover {color:#0099ff;}
	a:active {color: #0066cc;}
	a.button {text-decoration:none;}
	
	table.nav  {background-color: #dbddff;}
	table.body {margin-top:2ex; margin-bottom:2ex;}
	table.programlistingindent {margin-left:32px;}
	
	img { margin-bottom:0px; margin-top:0px;}
	tt {margin-left:0.5em; margin-right:0.5em; font-weight:lighter;}
	
	p {margin-top:0ex;}
	p.synopsis {margin-left:32px;}
	p.programlistingindent {margin-left:32px;}
	p.citetitle {margin-left:2em;}
	
	ul ul {list-style-type:square;}
	ul li p {margin-top:0ex; margin-bottom:.5ex; padding:0}
	ol li p {margin-top:0ex; margin-bottom:.5ex; padding:0}
	
	h1.reftitle {color:#a90000;}
	h1.reftitle {font-size:3.7ex; margin-top:0; margin-bottom:0; font-weight:bold}
	h1.title {color:black; font-size:4ex; margin-top:1ex; font-weight:bold}
	h2.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:3ex}
	h3.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2.5ex}
	h4.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2ex}
	h2 {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2.5ex}
	h3 {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2ex} 
	
	pre.programlisting {margin-left:32px;}
	pre.synopsis {margin-left:32px;}
	
	
	.categorytitle {margin-top:8px; padding-top:0px;}
	.categorylist {background-color: #e1e6f2;}
 	</style>
</head>
<body>
<a name="top_of_page"></a><p style="font-size:1px;"></p>
<h1 class="reftitle">mpt_demo_lti2</h1>
<h2>Purpose</h2>
<p>Demonstrates online MPC for LTI system</p>
<h2>Syntax</h2>
<pre class="synopsis">mpt_demo_lti2</pre>
<h2>Description</h2>
<p></p>
       Demonstrates online MPC for LTI system.
	<h2>Example(s)</h2>
<h3>Example 
				1</h3>Define an LTI prediction model <img src="../../../fig/mpt/demos/mpt_demo_lti21.png" alt="../../../fig/mpt/demos/mpt_demo_lti21.png">
      <pre class="programlisting">A = [1 1; 0 1]; B = [1; 0.5];</pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> lti = LTISystem('A', A, 'B', B); </pre>
<pre class="programlisting"></pre> Alternativelly, we can import from state-space objects: 
         <tt> s = ss(tf(1, [1 0 0])); </tt> 
      
         <tt> d = c2d(s, 1); </tt> 
      
         <tt> lti = LTISystem(d); </tt> 
       Define the MPC controller <pre class="programlisting"> horizon = 5; </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> ctrl = MPCController(lti, horizon); </pre>
<pre class="programlisting"></pre> Add state constraints <pre class="programlisting"> ctrl.model.x.min = [-5; -5]; </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> ctrl.model.x.max = [5; 5]; </pre>
<pre class="programlisting"></pre> Add input constraints <pre class="programlisting"> ctrl.model.u.min = -1; </pre>
<pre class="programlisting"></pre>
<pre class="programlisting"> ctrl.model.u.max = 1; </pre>
<pre class="programlisting"></pre> Set quadratic state penalty <pre class="programlisting"> ctrl.model.x.penalty = QuadFunction(eye(2)); </pre>
<pre class="programlisting"></pre> Set quadratic input penalty <pre class="programlisting"> ctrl.model.u.penalty = QuadFunction(1); </pre>
<pre class="programlisting"></pre> Obtain the optimal control input for a given initial condition.<pre class="programlisting"> x0 = [-4; 0]; Uonl = ctrl.evaluate(x0)</pre>
<pre class="programlisting">
Uonl =

     1

</pre>
<h2>See Also</h2>
<a href="./mpt_demo_lti1.html">mpt_demo_lti1</a>, <a href="./mpt_demo_lti3.html">mpt_demo_lti3</a>, <a href="./mpt_demo_lti4.html">mpt_demo_lti4</a>, <a href="./mpt_demo_lti5.html">mpt_demo_lti5</a><p></p>
<table class="nav" summary="Navigation aid" border="0" width="100%" cellpadding="0" cellspacing="0"><tr valign="top">
<td align="left" width="20">
<a href="mpt_demo_deployment_explicitmpctracking.html" class="button">&#9664;</a>  </td>
<td align="left">mpt_demo_deployment_explicitmpctracking</td>
<td>  </td>
<td align="right">mpt_demo_functions2</td>
<td align="right" width="20"><a href="mpt_demo_functions2.html" class="button">&#9654;</a></td>
</tr></table>
<br><p>©  <b>2003-2013</b>     Michal Kvasnica: STU Bratislava,    <a href="mailto:michal.kvasnica@stuba.sk">michal.kvasnica@stuba.sk</a></p>
</body>
</html>
